MAP 4XXX       Probability and Distribution Theory . . . . . 3(F,S)
Prerequisite: MAC 2313.
Mathematical methods of probability, conditional probability, stochastic independence; mathematical derivation of expectations, moment generating functions of discrete and continuous random variables, expectations, joint densities, marginal and conditional densities, conditional expectations; theory of probability inequalities, transformation of random variable’s order statostocs

MAP 4103        Mathematical Modeling . . . . . 3(S)
Prerequisite: MAP 2302
Mathematical models of physical problems leading to differential equations. Problems selected from biology, electrical circuitry, mechanics, etc. Methods of solution include Laplace transform, Fourier series, separation of variables and calculus of variations. (Gordon Rule Course: Theoretical Math)

MAP 4341        Partial Differential Equations  . . . . . 3(S)
Prerequisite: MAP 2302
First-order equations, derivation and classification of second-order equations. Solution techniques of boundary value and initial value problems; applications. (Gordon Rule Course: Theoretical Math)

MAP 4403        Mathematical Methods for Engineers . . . . . 3(CALL DEPT)
Prerequisite: MAP 2302
Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; Linear Algebra, including Gaussian elimination, determinants, inversion, linear independence, norms, inner product, orthogonality, Gram-Schmidt procedure, eigenvalues and eigenvectors, systems of differential equations

MAP 5XXX       Advanced Probability and Inferences . . . . . 3(S)
Prerequisite: MAC 2313
Advanced topics in probability, limit theorems, limiting distributions, order statistics, weak law of large numbers, strong law of large numbers, central limit theorem. Advanced topics in point and interval estimation, measures of quality of estimates, Exponential families, Completeness, Unbiasedness, Cramer-Rao inequality, Rao-Blackwell theorem, minimum variance unbiased estimators, maximum likelihood estimators principles, Bayes’ and minimax estimation, Robust estimation; Advanced hypothesis testing

MAP 5336        Ordinary Differential Equations . . . . . 3(F)
Prerequisite: MAA 4211 and MAA 4212
Fundamental existence theory, dependence of solutions on parameters, and stability

MAP 6XX3       Multivariate Analysis . . . . . 3(F)
Prerequisite: STA 4321, STA 5206, STA 5207
Eigenvalue decomposition; interpreting eigenvalues and eigenvectors; multivariate extensions of chi-square and t-tests; discrimination and classification procedures; multivariate analysis of variance; factor analysis; principal components analysis; applications to diagnostic problems in biological, medical, anthropological and social research

MAP 6XX4       Mathematical Methods of Operations Research I . . . . . 3(F)
Prerequisite: MAS 3105 or MAS 5107, and STA 4321
Mathematical linear programming models, theory of simplex method, revised simplex methods, dual simplex methods; duality theory and sensitivity analysis, transportation problems, theory of integer programming. May not be taken for credit by students having credit for STA 6607

MAP 6XX5       Mathematical Methods of Operations Research II . . . . .  3(S)
Prerequisite: MAP 6XX4 (Mathematical Methods of Operations Research I) or STA 6607
Interior-point algorithm, linear goal programming, game theory, nonlinear programming, network analysis, PERT/CPM, queuing theory. May not be taken for credit by students having credit for STA 6608

MAP 6106        Mathematical Methods of Operations Research I . . . . . 3(F)
Prerequisite: MAS 3105 or MAS 5107 and STA 4321
Mathematical probability models and distributions; linear programming models; the simplex method; duality and sensitivity analysis; inventory models; queuing theory; simulation. May not be taken for credit by students having credit for STA 6607

MAP 6107        Mathematical Methods of Operations Research II . . . . . 3(S)
Prerequisite: MAP 6106,
Decision theory and games, PERT/CPM, Markovian decision process integer programming, dynamic programming, reliability and maintenance. May not be taken for credit by students having credit for STA 6608